Table 3. Category 3: Sampling adaptively enhanced along one or more CVs.

Name	Description	Citations
aMD: accelerated MD	‘Boost’ potential applied when potential energy drops below a user-specified cut-off to increase rate of escape from minima. Reweighting of the resulting conformational ensemble to account for the applied bias is not always straightforward.	[92,145,146]
aUS: adaptive US	Iterates between sampling along a CV according to an umbrella potential and updating the umbrella potential according to an estimate of the probability distribution along the CV to improve sampling of under-sampled regions.	[147,148]
SH-US: self-healing US	Automatically updates the umbrella potential on-the-fly until the umbrella potentials cancel out the free energy profile.	[149]
Multidimensional aUS	Like aUS, but with the umbrella potentials applied across more than one CV.	[150]
Local elevation	Generates a history-dependent bias potential by adding Gaussians centred on the currently occupied value of one or more system properties to persuade the system to visit new areas of conformational space.	[93]
Conformational flooding	Like local elevation but formulated more generally to act on coarse-grained conformational coordinates.	[94]
LEUS: Local elevation umbrella sampling	A short LE build-up phase is used to construct an optimized biasing potential along conformationally relevant degrees of freedom that is then used in a (comparatively longer) US sampling phase.	[83]
Metadynamics	Like local elevation, but the biases are added to the free energy rather than potential energy surface, and the bias potential is generalised to act upon any CV or multidimensional set of CVs.	[95]
Multiple walkers (altruistic) metadynamics	Many metadynamics runs are performed in parallel, all of which contribute to filling in the free energy landscape.	[151]
WTE metadynamics: well-tempered ensemble metadynamics	The energy is used as collective variable to sample the well-tempered ensemble. Note that this is different to well-tempered metadynamics.	[152]
Bias-exchange metadynamics	A number of independent metadynamics simulations are run in parallel, each biasing a different CV, with exchange of coordinates between biases. The REMD and metadynamics act synergistically to overcome barriers.	[153]
Parallel-bias metadynamics	Single-replica variant of bias-exchange metadynamics in which the CV that is biased is switched during the simulation according to the Metropolis criterion, avoiding the need to have as many replicas as CVs.	[154]
T-REMD (parallel tempering) metadynamics	Multiple metadynamics simulations are performed in parallel at different temperatures, all of which contribute to filling in the free energy landscape. Improves the exploration of low probability regions and sampling of degrees of freedom not included in the CV, but requires a large number of replicas for all but very small systems.	[155]
REST metadynamics	Like T-REMD metadynamics, but only the solute experiences different temperatures.	[156]
WTE-metadynamics REMD	Combines WTE-metadynamics with T-REMD by running WTE-metadynamics at each temperature. Overlap and thus exchange between replicas is increased, and canonical averages of properties of interest can be obtained with reweighting.	[157]
Metadynamics with on-the-fly adjustment of the biasing frequency or weight
WT-metadynamics: well-tempered metadynamics	The height of the Gaussian functions and the rate at which they are deposited decreases during the simulation and inversely to the time spent at a given value of the CV(s) to prevent over-filling.	[158]
TT metadynamics: transition-tempered metadynamics	Like WT-metadynamics, but decreases the height of the Gaussians according to the number of round trips between basins in the free energy landscape. Useful for calculating the free energy surface along a few well-chosen collective variables (CVs) at a time, but requires a priori estimation of the basin positions.	[159]
µ-tempered metadynamics	Like WT-metadynamics, but allows use of wide Gaussians and a high filling rate without slowing convergence.	[160]
WT-metadynamics-REMD	Multiple WT-metadynamics simulations are run in parallel, each biasing multiple CVs simultaneously. The degree of bias increases across the ladder of replicas.	[161]
Metabasin metadynamics	The energy level to which the metadynamics can fill the free energy landscape is restricted, to either a pre-defined level or relative to unknown barrier energies, with both these and the Gaussian shape estimated on-the-fly. Reduces need to carefully choose CVs to avoid sampling irrelevant high-energy regions.	[162]
Metadynamics with on-the-fly adjustment of the biasing frequency or weight to achieve a target probability distribution function
OPES: on-the-fly probability-enhanced sampling	A recent reconsideration of metadynamics that begins with a coarse-grained estimate of the free energy landscape and converges towards a more detailed representation using a weighted kernel density estimation and on-the-fly compression algorithm.	[163]
VES: variationally enhanced sampling; deep-VES	Use an artificial neural network to determine a smoothly differentiable bias potential as a function of a pre-selected small number of CVs that drives the system towards a user-defined target probability distribution in which free energy barriers are lowered.	[164] [165]
TALOS: targeted adversarial learning optimized sampling	Uses a generative adversarial network competing game between a sampling engine and a virtual discriminator to construct the bias potential.	[166]